Biot-Savart law

J

B (r) = \frac{μ _{0}}{4 π} \int \frac{J ( r ^{'} ) \times ( r - r ^{'} )}{∣ r - r ^{'} ∣ ^{3}} d^{3} r^{'} .

On-axis magnetic field of a circular current loop

A circular loop of radius

R

I

has, on its axis,

B (z) = \frac{μ _{0} I R ^{2}}{2 ( R ^{2} + z ^{2} ) ^{3/2}} \overset{z}{^},

where the sign of

\overset{z}{^}

is fixed by the right-hand rule. At its centre,

B (0) = μ_{0} I / (2 R)

R

and

2 R

, separated by

D

, carry currents

I

and

2 I

in opposite senses, their on-axis fields cancel between the loops at distance

D /3

from the smaller loop.

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